在概率论方面我推荐：- Grimmett 写的《Probability and Random Processes》- David Williams 写的《Probability with Martingales》。从 Grimmett 开始看大概是个更好的选择，因为对前置数学知识的要求没那么高，而且涵盖的主题要丰富得多。Williams 那本更薄、更硬核，并且没有……
On the probability front I recommend: - Probability and Random Processes by Grimmett - Probability with Martingales by David Williams Grimmett is probably a better bet to start with since it doesn't expect quite as much prior math knowledge and covers a lot more topics. The Williams book is shorter, denser and doesn't…
……现成的。我自己没收集这些书单，不过我大概可以推荐：* Stephen Abbott 的《Understanding Analysis》，用于数学分析和一点实分析入门 * David Williams 的《Probability with Martingales》，适合进阶概率论 * Dym 和 McKean 的《Fourier Series and Integrals》。另外如果你只是泛泛地感兴趣，或许可以看看 Metacademy [1]，它提供了学习路线图……
…available. I don't maintain a collection of these, but I can probably recommend * Stephen Abbott, Understanding Analysis, for mathematical analysis and a little bit of real analysis * David Williams, Probability with Martingales, for advanced probability * Dym and McKean, Fourier Series and Integrals Alternatively if you have a more cursory interest, you can probably check out Metacademy [1] which provides roadmaps to learning…
……风格）。不管怎样，同时读几本讲同一主题的不同书是很有帮助的。- 有两本测度论概率论的书比很多常见的大部头要好读：Williams 的《Probability with Martingales》和 Pollard 的《A User's Guide to Measure-Theoretic Probability》。另外还有一本很棒的书叫《Probability through Problems》，它是通过一系列习题来展开理论的。
…style). It helps to read a few different books on the same topic simultaneously, anyway. - Two books on measure-theoretic probability theory that are more readable than many of the usual suspects are "Probability with Martingales" by Williams and "A User's Guide to Measure-Theoretic Probability" by Pollard. There is also a nice book called "Probability through Problems" that develops the theory through a series of exercises.
……比他的分析学书写得好多了，但这书挺厚的。不过课后习题很棒。至于概率论方面的书，我们大学时学的是《A Probability Path》。我当时不太喜欢。有人给我推荐过《Probability with Martingales》，虽然我没通读过，但看着非常棒。
…which is much better than his analysis book, but it's hefty. Good problems though. For a book on Probability, we read A Probability Path at my university. I wasn't fond of it. Someone referred me to Probability with Martingales, and though I didn't read it, it looked very good.
在概率论方面我推荐：- Grimmett 写的《Probability and Random Processes》- David Williams 写的《Probability with Martingales》。从 Grimmett 开始看大概是个更好的选择，因为对前置数学知识的要求没那么高，而且涵盖的主题要丰富得多。Williams 那本更薄、更硬核，并且没有……
On the probability front I recommend: - Probability and Random Processes by Grimmett - Probability with Martingales by David Williams Grimmett is probably a better bet to start with since it doesn't expect quite as much prior math knowledge and covers a lot more topics. The Williams book is shorter, denser and doesn't…
……现成的。我自己没收集这些书单，不过我大概可以推荐：* Stephen Abbott 的《Understanding Analysis》，用于数学分析和一点实分析入门 * David Williams 的《Probability with Martingales》，适合进阶概率论 * Dym 和 McKean 的《Fourier Series and Integrals》。另外如果你只是泛泛地感兴趣，或许可以看看 Metacademy [1]，它提供了学习路线图……
…available. I don't maintain a collection of these, but I can probably recommend * Stephen Abbott, Understanding Analysis, for mathematical analysis and a little bit of real analysis * David Williams, Probability with Martingales, for advanced probability * Dym and McKean, Fourier Series and Integrals Alternatively if you have a more cursory interest, you can probably check out Metacademy [1] which provides roadmaps to learning…
David Williams 的《Probability with Martingales》是我个人的心头好。而且绝不止我一个人这么觉得。
David Williams’ Probability with Martingales is a personal favourite. And I’m not the only one.
……风格）。不管怎样，同时读几本讲同一主题的不同书是很有帮助的。- 有两本测度论概率论的书比很多常见的大部头要好读：Williams 的《Probability with Martingales》和 Pollard 的《A User's Guide to Measure-Theoretic Probability》。另外还有一本很棒的书叫《Probability through Problems》，它是通过一系列习题来展开理论的。
…style). It helps to read a few different books on the same topic simultaneously, anyway. - Two books on measure-theoretic probability theory that are more readable than many of the usual suspects are "Probability with Martingales" by Williams and "A User's Guide to Measure-Theoretic Probability" by Pollard. There is also a nice book called "Probability through Problems" that develops the theory through a series of exercises.
……比他的分析学书写得好多了，但这书挺厚的。不过课后习题很棒。至于概率论方面的书，我们大学时学的是《A Probability Path》。我当时不太喜欢。有人给我推荐过《Probability with Martingales》，虽然我没通读过，但看着非常棒。
…which is much better than his analysis book, but it's hefty. Good problems though. For a book on Probability, we read A Probability Path at my university. I wasn't fond of it. Someone referred me to Probability with Martingales, and though I didn't read it, it looked very good.